Quantum Phase Constitutive Theory of Gravity: Deriving Newton’s Constant and the Equivalence Principle from Vacuum Rigidity

We present a derivation of Newton’s gravitational constant G from first principles within the Quantum Phase Constitutive Field Theory (QPCFT). By treating the vacuum as a constitutive medium with rigidity β = 1/4, we demonstrate that G = lp2c3/ℏ, where lp is the Planck length determined by the phase saturation scale of the Constitutive Quantum Phase Field (CQPF). This approach reinterprets gravity not as spacetime curvature, but as an emergent phenomenon arising from phase coupling between matter distributions. We apply this framework to the NASA vacuum chamber free-fall experiment, explaining the universal acceleration of objects with different compositions as a phase synchronization phenomenon. In the presence of a fluid medium, we introduce the concept of Phason Drag—dissipative phase interference causing differential fall rates. The theory predicts a detectable micro-vibration signature at approximately 1.6 GHz during fall in air, verifiable with current MEMS accelerometer technology. Our formalism reproduces all classical gravitational phenomena while resolving fundamental issues including the origin of G, the avoidance of singularities, and the unification of gravity with quantum mechanics without invoking extra dimensions.